On universal norms for $p$-adic representations in higher-rank Iwasawa theory
Volume 201 / 2021
Acta Arithmetica 201 (2021), 63-108
MSC: Primary 11F80, 11R23; Secondary 11R33.
DOI: 10.4064/aa200826-26-5
Published online: 11 October 2021
Abstract
We begin a systematic investigation of universal norms for $p$-adic representations in higher-rank Iwasawa theory. After establishing the basic properties of the module of higher-rank universal norms that naturally extend those in the classical theory, we construct an Iwasawa-theoretic pairing that is relevant to this setting. This allows us, for example, to refine the classical Iwasawa Main Conjecture for cyclotomic fields, and also to give applications to various well-known conjectures in arithmetic concerning Iwasawa invariants and leading terms of $L$-functions.
